We denote by \(\mathcal {P}_u(\mathbf {G})\)  the collection of (finite) unstable poles, i.e., located in \(\mathbb {C}\backslash \mathbb {S}\) , which belong to \(\mathbf {G}\in \mathbb {R}_p(\lambda )^{p \times m}\) . Moreover, we refer to \(\mathbf {G}\in \mathbb {R}_p(\lambda )^{p \times m}\)  as stable if \(\mathcal {P}_u(\mathbf {G})=\lbrace \emptyset \rbrace \) . Otherwise, we say that it is unstable. Note that \(\mathcal {P}_u(\mathbf {G})\)  includes repeated terms when the unstable poles of \(\mathbf {G}\)  have multiplicities greater than 1 (see section 6.5.3 of [1]}). Furthermore, we denote by \(\Lambda _u(A)\)  the collection of eigenvalues belonging to the matrix \(A\)  which are unstable, i.e., located in \(\mathbb {C}\backslash \mathbb {S}\) . Once again, \(\Lambda _u(A)\)  includes repeated terms when the unstable eigenvalues of \(A\)  have multiplicities greater than 1.
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